Perturbation Theory for Open Two-Level Nonlinear Quantum Systems

Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameterγ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rateγ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r=C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results.     

Nonlinear Quantum Mechanics at the Planck Scale

I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear effects can be of comparable magnitude to the linear ones and still be highly suppressed at low energies. This can offer alternative approaches to quantum gravity and to the evolution of the early universe. PACS: 04.60.-m, 03.65.Ta     

Quantum theory of nonlinear processes

Principles of development of the quantum theory of nonlinear processes on the basis of Lagrangian formulation are discussed. It is shown that in the framework of this formulation it is possible to preserve succession from the classical theory and, in particular, use these methods for studies of quantum systems. The quantum dispersion of a nonlinear oscillator excited by an external source and of a parametric generator is calculated. Its role is established in the solution of the problem of stability of oscillations.     

Quantum Set Theory

The complete orthomodular lattice of closed subspaces of a Hilbert space is considered as the logic describing a quantum physical system, and called a quantum logic. G. Takeuti developed a quantum set theory based on the quantum logic. He showed that the real numbers defined in the quantum set theory represent observables in quantum physics. We formulate the quantum set theory by introducing a strong implication corresponding to the lattice order, and represent the basic concepts of quantum physics such as propositions, symmetries, and states in the quantum set theory.     

Anthropic Interpretation of Quantum Theory

The problem of interpreting quantum theory on a large (e.g. cosmological) scale has been commonly conceived as a search for objective reality in a framework that is fundamentally probabilistic. The Everett programme attempts to evade the issue by the reintroduction of determinism at the global level of a state vector of the universe. The present approach is based on the recognition that, like determinism, objective reality is an unrealistic objective. It is shown how an objective theory of an essentially subjective reality can be set up using an appropriately weighted probability measure on the relevant set of Hilbert subspaces. It is suggested that an entropy principle (superseding the weak anthropic principle) should be used to provide the weighting that is needed. The application of this ansatz to a toy gedanken example (involving Schroedinger's legendary cat) is described in an appendix.     

瞬态光谱量子分析及其测量

介绍了新近研制的瞬态光谱测量仪,详细分析了瞬态光谱测量中的量子转换过程,进而表述出瞬态光谱信噪比表达式、图像参数和光电转换量子效率、光电成像有效积分时间和CCD光敏面的作用,最后给出了在此理论指导下的实测光谱曲线。     

Quantum Theory from Four of Hardy's Axioms

In a recent paper [e-print quant-ph/0101012], Hardy has given a derivation of quantum theory from five reasonable axioms. Here we show that Hardy's first axiom, which identifies probability with limiting frequency in an ensemble, is not necessary for his derivation. By reformulating Hardy's assumptions, and modifying a part of his proof, in terms of Bayesian probabilities, we show that his work can be easily reconciled with a Bayesian interpretation of quantum probability.     

电荷不连续时电容耦合介观电路的量子回路方程及其能谱

考虑电荷具有不连续性的事实对双LC介观电路进行量子化,给出耦合形式的量子回路方程以及无相互作用Hamilton本征基矢下的电路能谱.结果表明,计及电荷离散性将使回路方程的形式发生明显变化;介观电路的能谱除与电路参数相关外,还明显地依赖于电荷的量子化性质.     

Quantum Computation with Nonlinear Optics

We propose a scheme of quantum computation with nonlinear quantum optics. Polarization states of photons are used for qubits. Photons with different frequencies represent different qubits. Single qubit rotation operation is implemented through optical elements like the Faraday polarization rotator. Photons are separated into different optical paths, or merged into a single optical path using dichromatic mirrors. The controlled-NOT gate between two qubits is implemented by the proper combination of parametric up and down conversions. This scheme has the following features： （1） No auxiliary qubits are required in the controlled-NOT gate operation; （2） No measurement is required in the course of the computation; （3） It is resource efficient and conceptually simple.     

Characterizing Quantum Theory in Terms of Information-Theoretic Constraints

We show that three fundamental information-theoretic constraints—the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment—suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about nonlocality and bit commitment.     

On Models of Nonlinear Evolution Paths in Adiabatic Quantum Algorithms

In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model - an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.     

量子盘中的三阶非线性光学极化率

利用密度矩阵方法讨论了量子盘中的三阶非线性光学极化率,导出了近共振条件下的三次揩波的解析表达式,并以GaAs量子盘为例进行了具体的计算。结果表明,GaAs量子盘中的三阶非线性光学极化率要比GaAs量子阱的大几十倍。而且,选取适当的参量,可在吸收系数相对较小的情况下获得较大的折射率。     

量子阱非线性光学研究进展

综述了量子阱非线性光学领域近年来实验工作的进展，重点介绍了共振增强的二阶和三阶非线性效应、光折变效应、量子阱光调制器和ＩＶ族材料的非线性过程，指出该领域发展迅速，应用前景十分广阔。     

非线性简并光学参量放大系统的量子起伏

解析求解了P表象中考虑抽运吃空后的非线性含时简并光学参量放大系统获得压缩光所满足的福克尔-普朗克（Fokker-Planck）方程,并且计算了它在阈值附近及远离阈值的量子起伏。研究表明：若略去与η成正比的项,则通解很自然地过渡到线性近似解。计及与η成正比的项后,该解与Drummond等在阈值附近的微扰展开理论相比,基本相符。但在远离阈值处,微扰展开理论不适用,而该结果在阈值附近以及远离阈值的整个区域均是适用的。当μ→0压缩很小时,起伏趋近于真空起伏;而μ〉〉1,压缩增大时,趋近1／1＋μ线性理论。     

ZnS/CdSe量子点中线性和三阶非线性光吸收系数研究

在有效质量近似下,利用量子力学的密度矩阵理论,采用无限深势阱模型,从理论上研究了ZnS/CdSe柱型核壳结构量子点中线性和三阶非线性光吸收系数。导出了柱型量子点中线性和三阶非线性光学吸收系数的解析表达式,分析了该系统在不同条件下线性和三阶非线性光吸收系数与入射光频率之间的关系。改变系统的参数,该系统的光吸收系数呈规律性变化。计算结果表明:弛豫时间τ、入射光强I和壳半径R2对系统的吸收系数α有很大的影响,从而为实验上研究核壳结构量子点的非线性光学效应提供了必要的理论依据。     

Nonlinear Quantum Optical Springs and Their Nonclassical Properties

The original idea of quantum optical spring arises from the requirement of quantization of the frequencyof oscillations in the Hamiltonian of harmonic oscillator. This purpose is achieved by consideringa spring whose constant (and so its frequency) depends on the quantum states of another system.
Recently, it is realized that by the assumption of frequencymodulation ofω toω(1+μa^\dagger a)^1/2the mentioned idea can be established.
In the present paper, we generalize the approach of quantum optical springwith particular attention to thedependence of frequency to the intensity of radiation fieldthatnaturally observes in thenonlinear coherent states}, from which we arrive ata physical system has been called by us as nonlinear quantum optical spring.Then, after the introduction of the generalized Hamiltonian of nonlinear quantum optical spring and it's solution,we will investigate the nonclassical properties of the obtained states. Specially, typical collapse and revivalin the distribution functions and squeezing parameters, as particular quantum features, will berevealed.